Subgroups — #20241529

Order 6016.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689539	C₂	1	1	yes	maximal, characteristic
2	#15688957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#13094030	C₄	1	1	yes	characteristic
5	#13093964	C₄	1	1	yes	characteristic
6	#13093963	—	2	1	no	—
7	C₁₆×D₄₇	—	2	1	no	—
8	C₄₇⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
10	C₃₂×C₄₇	—	2	1	no	—
11	#10625350	C₈	1	1	yes	characteristic
12	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
13	#10625329	C₈	1	1	yes	characteristic
14	#10625324	—	2	1	no	—
15	C₈×D₄₇	—	2	1	no	—
16	C₁₆×C₄₇	D₄	1	1	yes	characteristic
17	C₁₆×C₄₇	D₄	1	1	yes	characteristic
18	C₄₇⋊C₁₆	—	2	1	no	—
19	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
20	C₂²⋊D₄₇	—	2	1	no	—
21	D₁₈₈	C₁₆	1	1	yes	characteristic
22	C₄×D₄₇	—	2	1	no	—
23	Dic₉₄	C₁₆	1	1	yes	characteristic
24	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₄₇	M₁₆	1	1	yes	characteristic
26	C₄₇⋊C₈	—	2	1	no	—
27	C₂²×C₄₇	M₃₂	1	1	yes	characteristic
28	C₂×D₄₇	—	2	1	no	—
29	C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
31	Dic₄₇	—	2	1	no	—
32	#1401	—	47	1	no	maximal, Sylow
33	C₂×C₄₇	—	2	1	no	—
34	C₂×C₄₇	C₂²⋊C₁₆	1	1	yes	characteristic
35	D₄₇	—	4	1	no	—
36	#504	—	47	1	no	—
37	M₆₄	—	47	1	no	—
38	C₂×C₃₂	D₄₇	1	1	yes	characteristic, complemented
39	C₄₇	#1401	1	1	yes	characteristic, complemented, Sylow
40	#131	—	47	1	no	—
41	M₃₂	—	47	1	no	—
42	M₃₂	—	94	1	no	—
43	C₂×C₁₆	—	94	1	no	—
44	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
45	C₃₂	—	2	1	no	—
46	C₃₂	—	94	1	no	—
47	#41	—	47	1	no	—
48	M₁₆	—	47	1	no	—
49	M₁₆	—	94	1	no	—
50	C₂×C₈	—	94	1	no	—
51	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
52	C₁₆	—	94	1	no	—
53	C₁₆	D₁₈₈	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
55	Q₈	—	47	1	no	—
56	D₄	—	47	1	no	—
57	D₄	—	94	1	no	—
58	C₂×C₄	—	94	1	no	—
59	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
60	C₈	—	94	1	no	—
61	C₈	#10625324	1	1	yes	characteristic
62	C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
63	C₂²	—	94	1	no	—
64	C₂²	#13093963	1	1	yes	characteristic
65	C₄	—	94	1	no	—
66	C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
67	C₄	C₁₆×D₄₇	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	188	1	no	—
70	C₂	(C₂×D₄₇)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₁₈₈
commutator	C₄×C₄₇	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₂×C₃₂×C₄₇	C₂
socle	C₂×C₄₇	C₂²⋊C₁₆
hypercenter	C₂×C₃₂	D₄₇
hypocenter	C₄₇	#1401
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #15688957	C₂	semidirect
3. C₂×C₃₂×C₄₇	C₂	semidirect
38. C₂×C₃₂	D₄₇	semidirect
39. C₄₇	#1401	semidirect